%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:49:07 PM UTC 2026
% Result : Theorem 1.59s 1.27s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 15 unt; 2 def)
% Number of atoms : 101 ( 66 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 40 ~; 30 |; 13 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 36 !; 2 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f7,conjecture,
! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& set_difference(X0,singleton(X1)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& set_difference(X0,singleton(X1)) = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( X0 != singleton(X1)
& X0 != empty_set
& set_difference(X0,singleton(X1)) = empty_set ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( ( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set )
& ( ( singleton(X1) != X0
& empty_set != X0 )
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f16,plain,
( sK2 != singleton(sK3)
& empty_set != sK2
& empty_set = set_difference(sK2,singleton(sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f10]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
sK2 != singleton(sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
empty_set = set_difference(sK2,singleton(sK3)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_58,negated_conjecture,
set_difference(sK2,singleton(sK3)) = empty_set,
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,negated_conjecture,
empty_set != sK2,
inference(cnf_transformation,[],[f27]) ).
tcf(c_60,negated_conjecture,
singleton(sK3) != sK2,
inference(cnf_transformation,[],[f26]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) != empty_set )
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(renaming,[status(thm)],[c_66]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = empty_set )
| ( singleton(X2) = X3 )
| ( X0 != X3 )
| ( singleton(X2) != X1 )
| ( set_difference(X0,X1) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_67]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( ( X0 = empty_set )
| ( singleton(X1) = X0 )
| ( set_difference(X0,singleton(X1)) != empty_set ) ),
inference(unflattening,[status(thm)],[c_159]) ).
tcf(c_223,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_224,definition,
iPr_def_11 = set_difference(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_225,negated_conjecture,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_60,c_223]) ).
tcf(c_226,negated_conjecture,
empty_set != sK2,
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_227,negated_conjecture,
iPr_def_11 = empty_set,
inference(demodulation,[status(thm)],[c_58,c_224]) ).
tcf(c_340,plain,
sK2 != iPr_def_11,
inference(light_normalisation,[status(thm)],[c_226,c_227]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_11 )
| ( singleton(X1) = X0 )
| ( set_difference(X0,singleton(X1)) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_160,c_227]) ).
tcf(c_351,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( singleton(sK3) = X0 )
| ( set_difference(X0,iPr_def_10) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_223,c_345]) ).
tcf(c_352,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ( X0 = iPr_def_10 )
| ( set_difference(X0,iPr_def_10) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_351,c_223]) ).
tcf(c_364,plain,
( ( sK2 = iPr_def_11 )
| ( sK2 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_224,c_352]) ).
tcf(c_366,plain,
sK2 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_364,c_340]) ).
tcf(c_369,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_225,c_366]) ).
tcf(c_370,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:22:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 1.59/1.27 % SZS status Started for theBenchmark.p
% 1.59/1.27 % SZS status Theorem for theBenchmark.p
% 1.59/1.27
% 1.59/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.59/1.27
% 1.59/1.27 % ------ iProver source info
% 1.59/1.27
% 1.59/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.59/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.59/1.27 % git: non_committed_changes: false
% 1.59/1.27
% 1.59/1.27 % ------ Parsing...
% 1.59/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.59/1.27
% 1.59/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.59/1.27
% 1.59/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.59/1.27
% 1.59/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.59/1.27 % ------ Proving...
% 1.59/1.27 % ------ Problem Properties
% 1.59/1.27
% 1.59/1.27 %
% 1.59/1.27 % clauses 11
% 1.59/1.27 % conjectures 3
% 1.59/1.27 % EPR 6
% 1.59/1.27 % Horn 10
% 1.59/1.27 % unary 10
% 1.59/1.27 % binary 0
% 1.59/1.27 % lits 13
% 1.59/1.27 % lits eq 10
% 1.59/1.27 % fd_pure 0
% 1.59/1.27 % fd_pseudo 0
% 1.59/1.27 % fd_cond 0
% 1.59/1.27 % fd_pseudo_cond 1
% 1.59/1.27 % AC symbols 0
% 1.59/1.27
% 1.59/1.27 % ------ Schedule dynamic 5 is on
% 1.59/1.27
% 1.59/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.59/1.27
% 1.59/1.27
% 1.59/1.27 % ------
% 1.59/1.27 % Current options:
% 1.59/1.27 % ------
% 1.59/1.27
% 1.59/1.27
% 1.59/1.27 %
% 1.59/1.27
% 1.59/1.27 % ------ Proving...
% 1.59/1.27 %
% 1.59/1.27
% 1.59/1.27 % SZS status Theorem for theBenchmark.p
% 1.59/1.27
% 1.59/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.59/1.27
% 1.59/1.27
%------------------------------------------------------------------------------